Double Penalized Quantile Regression for the Linear Mixed Effects Model

This paper proposes a double penalized quantile regression for linear mixed effects model, which can select fixed and random effects simultaneously. Instead of using two tuning parameters, the proposed iterative algorithm enables only one optimal tuning parameter in each step and is more efficient. The authors establish asymptotic normality for the proposed estimators of quantile regression coefficients. Simulation studies show that the new method is robust to a variety of error distributions at different quantiles. It outperforms the traditional regression models under a wide array of simulated data models and is flexible enough to accommodate changes in fixed and random effects. For the high dimensional data scenarios, the new method still can correctly select important variables and exclude noise variables with high probability. A case study based on a hierarchical education data illustrates a practical utility of the proposed approach.